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 A374387 a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal. 5

%I #9 Jul 10 2024 13:43:16

%S 1,0,-4,36,129,3340,2287607,162104000,16943055268,4059346088384,

%T 474967482901952,221630954408019520

%N a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Toeplitz_matrix">Toeplitz Matrix</a>.

%e a(5) = 3340:

%e [0, 5, 7, 3, 2]

%e [5, 0, 5, 7, 3]

%e [7, 5, 0, 5, 7]

%e [3, 7, 5, 0, 5]

%e [2, 3, 7, 5, 0]

%t a[n_]:=Max[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Prime[Range[n-1]]],i]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]

%Y Cf. A071079, A374341.

%Y Cf. A374386 (minimal), A374388 (maximal absolute value), A374389 (minimal nonzero absolute value).

%Y Cf. A374068 (minimal permanent), A374390 (maximal permanent).

%K sign,hard,more

%O 0,3

%A _Stefano Spezia_, Jul 07 2024

%E a(11) from _Giorgos Kalogeropoulos_, Jul 10 2024

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Last modified September 11 02:28 EDT 2024. Contains 375813 sequences. (Running on oeis4.)